Chapter 18 - Gravitational fields Flashcards
what is the range of gravity
infinite
Closer gravitational lines mean
stronger field
define gravitational field strength, g
gravitational force experienced per unit mass by an object at that point in a gravitational field
equation for g
F/m
What is the only condition for the equation for g
the object needs to be small enough that the internal gravitational field is negligible compared to the external gravitational field
Newtons law of gravitation
two point masses attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of their separation
Newtons equation for gravitation
F = -GMm/r^2
why is the G minus in the equation for gravitation
gravity is an attractive force
gravitational field strength for a point mass
g = GM/r^2
Keplers first law
the orbit of a planet is an ellipse. with the sun at one focus, however the eccentricity of the ellipse is very low so the motion can be modeled as circular
Keplers second law
a line segment joining a planet and the sun sweeps out equal areas during equal time intervals
Keplers third law
the square of the orbital period T is proportional to the cube of the average distance r from the sun. T^2 α r^3
How does keplers second law stand
objects move faster when it is closer to the sun
derive equation regarding period of orbit for keplers laws
F = mv^2/r = GMm/r^2 GM/r = v^2 as v = 2πr/T GM/r = 4πr^2r^3/t^2 T^2 = 4π^2r^3/GM where M is the solar mass T is the period of orbit therefore T^2 α r^3
What is a satellite
an object orbiting another object, e.g. moon or ISS
Outline a geostationary satellite
- have an orbital period of one day
- travel in the same direction as the rotation of the earth
- Travel along the equatorial plane
- remain above the same point on the earths surface
- useful for communications and surveying as they have constant coverage
define gravitational potential, Vg with equation
work done per unit mass to move an object from infinity to that point
V(g) = -GM/r
what causes a change in gravitational potential
moving towards the object reduces gravitational potential
moving away increases potential
Define gravitational potential energy
E = mV(g) = -GMm/r, work done in moving a mass from infinity to that point in a gravitational field
Escape Velocity
For an object to escape a gravitational field produced by a mass, the kinetic energy of the object at the start must be equal to or greater the the GPE required to lift it to infinity. Therefore the speed required to exit the gravitational pull.
derive equation for escape velocity
KE = 1/2mv^2 = GMm/r
so v = √(2GM/r)
